The actuaries wrote that "policymakers should consider the potential adverse consequences of eliminating the mandate."
Those consequences include "increases in premium and the number of uninsured, unless adequate alternative mechanisms are implemented," the letter said.
"Eliminating the mandate would have significant implications for health insurance coverage," the group wrote.
The mandate imposes a tax penalty for Americans who fail to have some form of health coverage during the year.
The Congressional Budget Office has estimated that if the mandate is killed, 13 million more people would become uninsured than are currently projected.
In turn, premium prices are estimated to increase in future years by an extra 10 percent because the remaining pool of Obamacare customers will be sicker and older than it would have been with the mandate still in effect.
Those higher premiums will be paid, as a rule, by higher-income customers who do not receive federal tax credits that reduce their premium costs.
But because premium prices for 2018 are already set, repealing the mandate soon could mean that healthier customers would drop off coverage, leaving insurers with costly, sicker customers.
"This could result in insurer losses and solvency concerns," the actuaries wrote.
The letter also warned that increased uncertainty and instability in the Obamacare market as a result of mandate repeal would increase the risk of insurer losses in future years.
And that "could cause an increase in insurer withdrawals from the market," the letter said.
Republican Senate leaders want the mandate repealed because it would save the federal government almost $340 billion in spending over the next decade.
Those savings — which stem from the government having to subsidize fewer Obamacare customers' premium costs — could then be used to fund tax reductions included in the pending bill.
In some cases, an Obamacare customer whose premiums were raised because the mandate was repealed would see tax reductions that equaled, or more than equaled the difference in their premiums.
But some Obamacare customers would not get enough in the way of a tax break to cover the difference form the higher premiums.
A customer's age, income and state of residence will affect which group they fall into.
In an analysis published Tuesday, the Commonwealth Fund said 27-year-old, nonsubsidized Obamacare customers would see an average premium hike of $492 annually in 2019, and $729 annually in 2027 if the mandate is repealed.
An average 40-year-old customer would see an increase of $598 per year in 2019, rising to $883 in 2027, the group said.
And 60-year-olds would see an increase of $1,269 in 2019, and $1,875 in 2027, according to the analysis.